We now need to define \(\widetilde{g}_{\Theta }\) . Given a latent vector \(\textbf {z}\)  and the GCNN of Section REF  with weights \(\Theta \) , we can approximate the performance by feeding the triangulated mesh \(\textbf {P}(\textbf {z})\)  to the network to produce an estimated field of values \(\tilde{\textbf {y}}\)  and an estimated performance value \(\tilde{r}=R(\tilde{\textbf {y}})\) . We take this to be the estimate that \(\widetilde{g}_{\Theta }\)  but we also need an uncertainty estimate in the form of a variance, which means assessing the reliability of our network. Among all the methods that can be used to assess to this end, MC-Dropout [1]} and Deep Ensembles [2]} have emerged as two of the most popular ones. MC-Dropout involves randomly zeroing out network weights and assessing the effect, whereas Ensembles involve training multiple networks starting from different initial conditions. In practice, the latter tends to perform better but also to be more computationally demanding due to the requirement of restarting the training procedure from scratch many times.
